Algebra Two Honors

Summer Packet Remediation

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Unit 1

• Converting a Recursive Sequence into an Explicit Formula
• Finding the nth Element of a Recursive Sequence - 3 Methods
• Using Slope to Talk About Linear Data Sets
• Doing a Linear Regression on Your Calculator.
• (Finding the) Equation of a Line in Slope-Intercept Form:
  • when given a point on the line and the slope (y=mx+b) (y=a+bx)
  • when given two points on the line (y=mx+b) (y=a+bx)
  • when given a point on the line and a parallel line (y=mx+b) (y=a+bx)
  • when given a point on the line and a perpendicular line (y=mx+b) (y=a+bx)
    
    
• Solving Linear Systems using the Graphical Method (TI-83/4)
• Solving Linear Systems using the Substitution Method
• Solving Linear Systems using the Addition Method (AKA the Elimination Method)
• Linear System Word Problems
• Solving Systems of Inequalities

Unit 2

• Squaring Binomials
• Expanding Binomials and Monomials
• Function Evaluation
• Performing Function Composition when Given Two Functions
• Reading Function Values when Given a Graph
• Graphing a Function Using a Transformation
• Writing an Equation of a Graph Using Transformations
• Writing Equations of Circles in Standard Form - Completing the Square
• Writing Equations of Ellipses in Standard Form

Unit 3

• Multipliers - What They Are and How to Determine Them
• Writing and Using Exponential Functions - Basic writing of an equation when given the initial value and info about the multiplier. Also shows estimating the doubling time on the calculator
• Writing and Using Exponential Functions - Writing of an equation when given the initial value and info about the multiplier. This problem has an adjusted period
• Writing and Using and Exponential Function - Finding Doubling Time Using Log
• Writing Exponential Functions - Using Point Ratio Form - Given two points - work backwards to find the function
• Writing Exponential Functions - Given two points - work backwards to find the function
• Solving Equations with Rational Exponents
• Solving Equations with Variables in the Exponent - Feel Method
• Solving Equations with Variables in the Exponent - Common Base and 1:1 Principle
• Solving Equations with Variables in the Exponent - Logs

Unit 4

• Overview of Factoring
• Factoring -Greatest Common Factor (GCF or Undistribution)
• Factoring - Difference of Two Squares
• Factoring - Perfect Square Trinomials
• Factoring - Quadratic Trinomials of the form x^2+bx+c. (Factors of c that add up to b)
• Factoring - Quadratic Trinomials of the form ax^2+bx+c where a is not 1.
  • Tic-Tac-Toe Method
  • Box Method (This is the one that I do in class the others are alternative methods)
  • Box Method with Program
  • Fractions Method
  • Grouping Method
• Factoring - Sum and Differences of Cubes
• Determining the Degree and Equation of the Polynomial that Models a Data Set
• Solving Quadratic Equations
  • When Asked to Use the Zero Product Property
  • When Asked to Use the Quadratic Formula
  • When Asked to Extract the Root
  • When No Particular Method is Indicated
  
  
• Determining the 5 Point Graph of a Quadratic when Given:
  • Given Factored Form
  • Given General/Standard Form
  • Given Vertex Form
  
  
• Converting from General Form to Vertex Form - Completing the Square
• Simplifying Radicals with Negative Radicands - Imaginary Numbers
• Distribute and FOIL with Imaginary Numbers
• Using and Understanding the Discriminant
• Quadratic Word Problems
  • Basic Area Problem
  • Changing Area Problem - Extending the Length and Width of a Rectangle Equally
  • Area of a Bordered Rectangle - Lace on a Table Cloth

Flipped Classroom Materials

• Module 1 - Radicals
• Module 2 - Factoring

Remediation

• Exponent Rules for Multiplying
• Distribute, FOIL and Multiplying Quantities
• Simplifying Through Distribution or FOIL and Collecting Like Terms

Emergency Lesson Videos

• Expanding Binomials and Monomials
• Determining the GCF and LCM of a set of Numbers
• Simplifying Square Roots to Exact Answers

Out of Date Material

• Multiplying a 2x2 Matrix by a 2x2 Matrix
• Solving a Linear System with Matrix Inverses on Your Calculator
• Solving Absolute Value Equations
• Solving Absolute Value Inequalities
• Solving Value Equations/Inequalities - Special Examples - Null Set and All Real Numbers

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Algebra Prep/One

Unit 1

Unit 2

Solving Equations

• Solving Equations Using the DUR Method
• Solving Two Step Equations
• Solving Equations with Variables on Both Sides
• Solving Equations Using the Five Step Method - DCG01
• Solving Equations Using the Five Step Method - DCG01 - Tricky Distribution Example
• Solving Equations Using the Five Step Method - DCG01 - with Fractions
• Solving Equations Using the Ti-83-Ti84 (Graphical Method)
• Solving Literal Equations (Basic)
• Solving Literal Equations (Collecting Like Terms Required)
• Solving Proportions (Cross Multiplication)
• Solving Proportions (Cross Multiplication) ...problems involving Distribution

Unit 3

Solving Linear Inequalities

• Graphing Inequalities in One Variable
• Solving Inequalities in One Variable - DCG01*
• Solving Inequalities in One Variable - Flipping the Symbol
• Graphing Compound Inequalities

Unit 4

Data

• Computing a 5 Point Data Summary on the Calculator

Unit 5a

• Determining if a Data Set is Linear or Not Using the Idea of Rate of Change
• Determining if the Rate of Change of a Graph is Constant or Variable

Unit5b

Slope and Lines

Unit 6

Solving Linear Systems

• Solving Linear Systems Using the Graphical Method -Given y=mx+b form
• Solving Linear Systems Using the Graphical Method - NOT Given y=mx+b form
• Solving Linear Systems Using the Addition Method - Given Opposite Coefficients
• Solving Linear Systems Using the Addition Method - NOT Given Opposite Coefficients
• Solving Linear Systems Using the Substitution Method - Given One Variable Isolated
• Solving Linear Systems Using the Substitution Method - NOT Given One Variable Isolated
• Checking Solutions to Linear Systems on Your Calculator
• Graphing Linear Inequalities in One or Two Variables in the XY Plane (Test Point Required)
• Graphing Systems of Inequalities (No Test Point Required)

Unit 7

Unit 8

• Overview of Factoring
• Greatest Common Factor (GCF or Undistribution)
• Difference of Two Squares
• Perfect Square Trinomials
• Quadratic Trinomials of the form x^2+bx+c. (Factors of c that add up to b)
• Quadratic Trinomials of the form ax^2+bx+c
  • Tic-Tac-Toe Method
  • Box Method (This is the one that I do in class the others are alternative methods)
  • Box Method with Program
  • Fractions Method
  • Grouping Method

Unit 9

• Determining if a Relation, Mapping or Graph is Function
• Determining the Domain and Range of a Relation/Function
• Function Evaluation - Single Evaluation
• Function Evaluation - Double Evaluation
• Function Composition
• Function Inverses - Determining the Inverse from a Relation or Graph
• Function Inverses - Determining the Inverse from an Equation

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Trig Pre-Calc

Diagnostic Remediation

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Unit 1

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• Expanding Binomials and Monomials
• Determining the Domain of a Function When Given a Graph
• Determining the Excluded Values of a Function (Rational and Square Root Functions)
• Reading Function Values when Given a Graph
• Performing Function Composition when Given Two Functions.
• Determining if Two Functions are Inverses of Each Other
• Computing the Inverse Function of a Given Function
• Computing the Distance Between Two Points with the Distance Formula
• Computing the Midpoint Between Two Points with the Midpoint Formula(Start this video at 1:15 to get past the introduction.)
• Overview of Equations of Lines
• Finding the Equation of a Line in Slope-Intercept Form:
  • when a given a point on the line and the slope (y=mx+b)
  • when given two points on the line (y=mx+b)
  • when given a point on the line and a parallel line (y=mx+b)
  • when given a point on the line and a perpendicular line (y=mx+b)

Unit 2

• Even and Odd Functions
• Graphing Rational Functions
• Determining the Intercepts of a Rational Function
• Determining the Equation of a Vertical Asymptote in a Rational Function
• Determining the Equation of a Horizontal Asymptote in a Rational Function
• Determining the Location of a Hole in a Rational Function
• Graphing a Rational Function (No Holes)
• Graphing a Rational Function (with Holes)
• Computing the Derivative Using the Power Rule
• Computing the Slope at a Point
• Finding the Equation of the Tangent Line to the Curve
• Finding Max, Min and Points of Inflections with the Derivative
• Finding Point(s) on a Curve with a Given Slope

Unit 3

Imaginary Numbers

• Simplifying Radicals with Negative Radicands - Imaginary Numbers
• Distribute and FOIL with Imaginary Numbers
• Quadratic Formula with Imaginary Numbers

• Solving Quadratics by Completing the Square (Easy and Hard Example)
• Sketching Polynomials Using End Behavior and Intercepts
• Writing Polynomial Equations From Their Graphs
• Solving Radical Equations
• Solving Rational Equations

Synthetic Division and Remainder Theorem

• The Remainder Theorem (Finding Remainders of Polynomial Division and Determining if a Given Binomial is a Factor to a Given Polynomial)
• Synthetic Division of Polynomials
• Using Synthetic Division to Determine if a Linear Binomial is a Factor of Given Polynomial

Unit 4

• What is a radian? (E.R.)
• What is Standard Position and a Coterminal Angle?
• Converting Degrees and Radians (E.R)
• The Six Basic Trig Functions (E.R.)
• Reference Angles
• Knowing the Sign of a Trig Value Based on the Quadrants (ASTC - ALL STUDENTS TAKE CALCULUS)
• Knowing the Sign of a Trig Value Based on the Quadrants - Examples
• Finding the Value of the Other Five Trig Functions When Given One Value
• Memorizing the Trig Functions of Special Angles
• Determining the Exact Value of A Trig Function - Unit Circle
• Determining the Exact Value of a Trig Function - Special Angle
• Law of Sines - No Ambiguous Case
• Law Of Cosines

Unit 5

• Graphing the Parent Functions of Sin and Cos
• Graphing the Parent Functions of Sin and Cos - shortened version
• Graphing Transformations of Sin and Cos without a Change of Period - (on graph paper)
• Graphing Sin and Cos Transformations that Have a Change of Period
• Solving Trig Equations with Exact Values without Factoring
• Solving Trig Equations with Exact Values Using Factoring
• Solving Trig Equations with your Calculator
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Unit 6

Old Unit Two - Prior to Spring 2016

• Solving Linear Systems using the Graphical Method (TI-83/4)
• Solving Linear Systems using the Substitution Method
• Solving Linear Systems using the Addition Method (AKA the Elimination Method
• Multiplying a 2x2 Matrix by a 2x2 Matrix
• Solving a Linear System with Matrix Inverses on Your Calculator